Robust Design Optimization of Viscoelastic Damped Composite Structures Integrating Model Order Reduction and Generalized Stochastic Collocation

This study presents a novel approach that integrates model order reduction (MOR) and generalized stochastic collocation (gSC) to enhance robust design optimization (RDO) of viscoelastic damped composite structures under material and geometric uncertainties. The proposed methodology systematically reduces computational burden while maintaining the required accuracy. A projection-based MOR is chosen to alleviate the substantial computational costs associated with nonlinear eigenvalue problems. To minimize the sampling size for uncertainty propagation (UP) while effectively addressing diverse probability density distributions, a gSC method incorporating statistical moment computation techniques is developed. Pareto optimal solutions are determined by combining the proposed MOR and gSC approaches with a well-established Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm, which accounts for robustness in handling design variables, objectives, and constraints. The results of the four examples illustrate the efficacy of the proposed MOR and gSC methods, as well as the overall RDO framework. Notably, the findings demonstrate the feasibility of this approach for practical applications, driven by a significant reduction in computational costs. This establishes a solid foundation for addressing complex optimization challenges in real-world scenarios characterized by various uncertainties.